Decorrelation-Based Feature Discovery: ARCENE-Whole
Jose Tamez
2023-09-29
- 1 Effect of UPSTM-Based Decorrelation
on Feature Discovery
- 1.0.1 Loading the libraries
- 1.1 Material
- 1.2 The Data
- 1.3 Generaring the report
- 1.4 The heatmap of the data
- 1.5 The decorrelation
- 1.6 The heatmap of the decorrelated data
- 1.7 The correlation matrix after decorrelation
- 1.8 U-MAP Visualization of features
- 1.9 Univariate Analysis
- 1.10 Comparing ILAA vs PCA vs EFA
- 1.11 Effect on CAR modeling
1 Effect of UPSTM-Based Decorrelation on Feature Discovery
1.0.1 Loading the libraries
library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)
op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)1.1 Material
1.2 The Data
trainLabeled <- read.delim("~/GitHub/FCA/Data/trainSet.txt")
validLabeled <- read.delim("~/GitHub/FCA/Data/arcene_valid.txt")
wholeArceneSet <- rbind(trainLabeled,validLabeled)
wholeArceneSet$Labels <- 1*(wholeArceneSet$Labels > 0)
wholeArceneSet[,1:ncol(trainLabeled)] <- sapply(wholeArceneSet,as.double)
1.2.0.1 Standarize the names for the reporting
studyName <- "ARCENE"
dataframe <- wholeArceneSet
outcome <- "Labels"
thro <- 0.8
cexheat = 0.10
TopVariables <- 101.3 Generaring the report
1.3.1 Libraries
Some libraries
library(psych)
library(whitening)
library("vioplot")
library("rpart")1.3.2 Data specs
pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))| rows | col |
|---|---|
| 200 | 10000 |
pander::pander(table(dataframe[,outcome]))| 0 | 1 |
|---|---|
| 112 | 88 |
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
largeSet <- length(varlist) > 1500 1.3.3 Scaling the data
Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns
### Some global cleaning
sdiszero <- apply(dataframe,2,sd) > 1.0e-16
dataframe <- dataframe[,sdiszero]
varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
dataframe <- dataframe[,tokeep]
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples
dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData1.4 The heatmap of the data
numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000
if (!largeSet)
{
hm <- heatMaps(data=dataframeScaled[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
xlab="Feature",
ylab="Sample",
srtCol=45,
srtRow=45,
cexCol=cexheat,
cexRow=cexheat
)
par(op)
}1.4.0.1 Correlation Matrix of the Data
The heat map of the data
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
#cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
cormat <- cor(dataframe[,varlist],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Original Correlation",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
diag(cormat) <- 0
print(max(abs(cormat)))
}1.5 The decorrelation
DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#>
#> V3351 V3174 V5124 V7607 V2680 V1623
#> V1 V3 V4 V5 V6 V7
#> 0.7046980 0.2306402 0.4581828 0.7383841 0.2617450 0.8979091
#>
#> Included: 7748 , Uni p: 1.539409e-05 , Base Size: 1008 , Rcrit: 0.2901451
#>
#>
1 <R=1.000,thr=0.950>, Top: 289< 20 >..[Fa= 289 ]( 289 , 2768 , 0 ),<|><>Tot Used: 3057 , Added: 2768 , Zero Std: 0 , Max Cor: 1.000
#>
2 <R=1.000,thr=0.950>, Top: 894< 32 >........[Fa= 1170 ]( 881 , 2252 , 289 ),<|><>Tot Used: 4838 , Added: 2252 , Zero Std: 0 , Max Cor: 1.000
#>
3 <R=1.000,thr=0.950>, Top: 790< 19 >.......[Fa= 1944 ]( 781 , 1609 , 1170 ),<|><>Tot Used: 5714 , Added: 1609 , Zero Std: 0 , Max Cor: 1.000
#>
4 <R=1.000,thr=0.950>, Top: 496< 17 >....[Fa= 2428 ]( 492 , 1055 , 1944 ),<|><>Tot Used: 6209 , Added: 1055 , Zero Std: 0 , Max Cor: 1.000
#>
5 <R=1.000,thr=0.950>, Top: 325< 37 >...[Fa= 2747 ]( 321 , 656 , 2428 ),<|><>Tot Used: 6480 , Added: 656 , Zero Std: 0 , Max Cor: 1.000
#>
6 <R=1.000,thr=0.950>, Top: 196< 15 >.[Fa= 2941 ]( 196 , 345 , 2747 ),<|><>Tot Used: 6579 , Added: 345 , Zero Std: 0 , Max Cor: 0.999
#>
7 <R=0.999,thr=0.950>, Top: 104< 4 >.[Fa= 3044 ]( 103 , 173 , 2941 ),<|><>Tot Used: 6624 , Added: 173 , Zero Std: 0 , Max Cor: 0.999
#>
8 <R=0.999,thr=0.950>, Top: 49< 9 >[Fa= 3093 ]( 49 , 82 , 3044 ),<|><>Tot Used: 6642 , Added: 82 , Zero Std: 0 , Max Cor: 0.998
#>
9 <R=0.998,thr=0.950>, Top: 23< 4 >[Fa= 3116 ]( 23 , 41 , 3093 ),<|><>Tot Used: 6647 , Added: 41 , Zero Std: 0 , Max Cor: 0.997
#>
10 <R=0.997,thr=0.950>, Top: 12< 3 >[Fa= 3128 ]( 12 , 17 , 3116 ),<|><>Tot Used: 6649 , Added: 17 , Zero Std: 0 , Max Cor: 0.982
#>
11 <R=0.982,thr=0.950>, Top: 2< 1 >[Fa= 3130 ]( 2 , 2 , 3128 ),<|><>Tot Used: 6649 , Added: 2 , Zero Std: 0 , Max Cor: 0.950
#>
12 <R=0.950,thr=0.900>, Top: 1316< 1 >............[Fa= 3471 ]( 1275 , 1651 , 3130 ),<|><>Tot Used: 6725 , Added: 1651 , Zero Std: 0 , Max Cor: 0.999
#>
13 <R=0.999,thr=0.950>, Top: 223< 1 >..[Fa= 3531 ]( 223 , 223 , 3471 ),<|><>Tot Used: 6725 , Added: 223 , Zero Std: 0 , Max Cor: 0.986
#>
14 <R=0.986,thr=0.950>, Top: 14< 1 >[Fa= 3533 ]( 14 , 14 , 3531 ),<|><>Tot Used: 6725 , Added: 14 , Zero Std: 0 , Max Cor: 0.953
#>
15 <R=0.953,thr=0.950>, Top: 1< 1 >[Fa= 3533 ]( 1 , 1 , 3533 ),<|><>Tot Used: 6725 , Added: 1 , Zero Std: 0 , Max Cor: 0.950
#>
16 <R=0.950,thr=0.900>, Top: 545< 3 >.....[Fa= 3619 ]( 535 , 606 , 3533 ),<|><>Tot Used: 6747 , Added: 606 , Zero Std: 0 , Max Cor: 0.998
#>
17 <R=0.998,thr=0.950>, Top: 85< 1 >[Fa= 3631 ]( 85 , 85 , 3619 ),<|><>Tot Used: 6747 , Added: 85 , Zero Std: 0 , Max Cor: 0.996
#>
18 <R=0.996,thr=0.950>, Top: 8< 1 >[Fa= 3632 ]( 7 , 7 , 3631 ),<|><>Tot Used: 6747 , Added: 7 , Zero Std: 0 , Max Cor: 0.950
#>
19 <R=0.950,thr=0.900>, Top: 159< 1 >.[Fa= 3646 ]( 156 , 165 , 3632 ),<|><>Tot Used: 6756 , Added: 165 , Zero Std: 0 , Max Cor: 0.996
#>
20 <R=0.996,thr=0.950>, Top: 30< 1 >[Fa= 3652 ]( 30 , 30 , 3646 ),<|><>Tot Used: 6756 , Added: 30 , Zero Std: 0 , Max Cor: 0.949
#>
21 <R=0.949,thr=0.900>, Top: 54< 1 >[Fa= 3653 ]( 48 , 49 , 3652 ),<|><>Tot Used: 6758 , Added: 49 , Zero Std: 0 , Max Cor: 0.994
#>
22 <R=0.994,thr=0.950>, Top: 9< 1 >[Fa= 3655 ]( 9 , 9 , 3653 ),<|><>Tot Used: 6758 , Added: 9 , Zero Std: 0 , Max Cor: 0.958
#>
23 <R=0.958,thr=0.950>, Top: 1< 1 >[Fa= 3655 ]( 1 , 1 , 3655 ),<|><>Tot Used: 6758 , Added: 1 , Zero Std: 0 , Max Cor: 0.948
#>
24 <R=0.948,thr=0.900>, Top: 8< 1 >[Fa= 3655 ]( 8 , 8 , 3655 ),<|><>Tot Used: 6758 , Added: 8 , Zero Std: 0 , Max Cor: 0.956
#>
25 <R=0.956,thr=0.950>, Top: 1< 1 >[Fa= 3655 ]( 1 , 1 , 3655 ),<|><>Tot Used: 6758 , Added: 1 , Zero Std: 0 , Max Cor: 0.917
#>
26 <R=0.917,thr=0.900>, Top: 2< 1 >[Fa= 3655 ]( 2 , 2 , 3655 ),<|><>Tot Used: 6758 , Added: 2 , Zero Std: 0 , Max Cor: 0.907
#>
27 <R=0.907,thr=0.900>, Top: 1< 1 >[Fa= 3655 ]( 1 , 1 , 3655 ),<|><>Tot Used: 6758 , Added: 1 , Zero Std: 0 , Max Cor: 0.900
#>
28 <R=0.900,thr=0.800>, Top: 1170< 1 >...........[Fa= 3833 ]( 1108 , 1482 , 3655 ),<|><>Tot Used: 6793 , Added: 1482 , Zero Std: 0 , Max Cor: 0.993
#>
29 <R=0.993,thr=0.950>, Top: 40< 1 >[Fa= 3844 ]( 40 , 42 , 3833 ),<|><>Tot Used: 6793 , Added: 42 , Zero Std: 0 , Max Cor: 0.950
#>
30 <R=0.950,thr=0.900>, Top: 132< 1 >.[Fa= 3867 ]( 129 , 129 , 3844 ),<|><>Tot Used: 6793 , Added: 129 , Zero Std: 0 , Max Cor: 0.965
#>
31 <R=0.965,thr=0.950>, Top: 2< 1 >[Fa= 3867 ]( 2 , 2 , 3867 ),<|><>Tot Used: 6793 , Added: 2 , Zero Std: 0 , Max Cor: 0.947
#>
32 <R=0.947,thr=0.900>, Top: 7< 1 >[Fa= 3868 ]( 7 , 7 , 3867 ),<|><>Tot Used: 6793 , Added: 7 , Zero Std: 0 , Max Cor: 0.900
#>
33 <R=0.900,thr=0.800>, Top: 413< 1 >...[Fa= 3907 ]( 366 , 415 , 3868 ),<|><>Tot Used: 6801 , Added: 415 , Zero Std: 0 , Max Cor: 0.979
#>
34 <R=0.979,thr=0.950>, Top: 7< 1 >[Fa= 3909 ]( 7 , 7 , 3907 ),<|><>Tot Used: 6801 , Added: 7 , Zero Std: 0 , Max Cor: 0.950
#>
35 <R=0.950,thr=0.900>, Top: 29< 1 >[Fa= 3912 ]( 29 , 29 , 3909 ),<|><>Tot Used: 6801 , Added: 29 , Zero Std: 0 , Max Cor: 0.899
#>
36 <R=0.899,thr=0.800>, Top: 74< 2 >[Fa= 3919 ]( 64 , 74 , 3912 ),<|><>Tot Used: 6803 , Added: 74 , Zero Std: 0 , Max Cor: 0.921
#>
37 <R=0.921,thr=0.900>, Top: 3< 1 >[Fa= 3919 ]( 3 , 3 , 3919 ),<|><>Tot Used: 6803 , Added: 3 , Zero Std: 0 , Max Cor: 0.924
#>
38 <R=0.924,thr=0.900>, Top: 1< 1 >[Fa= 3920 ]( 1 , 1 , 3919 ),<|><>Tot Used: 6803 , Added: 1 , Zero Std: 0 , Max Cor: 0.900
#>
39 <R=0.900,thr=0.800>, Top: 19< 1 >[Fa= 3920 ]( 15 , 15 , 3920 ),<|><>Tot Used: 6804 , Added: 15 , Zero Std: 0 , Max Cor: 0.988
#>
40 <R=0.988,thr=0.950>, Top: 2< 1 >[Fa= 3921 ]( 2 , 2 , 3920 ),<|><>Tot Used: 6804 , Added: 2 , Zero Std: 0 , Max Cor: 0.931
#>
41 <R=0.931,thr=0.900>, Top: 1< 1 >[Fa= 3921 ]( 1 , 1 , 3921 ),<|><>Tot Used: 6804 , Added: 1 , Zero Std: 0 , Max Cor: 0.910
#>
42 <R=0.910,thr=0.900>, Top: 1< 1 >[Fa= 3922 ]( 1 , 1 , 3921 ),<|><>Tot Used: 6804 , Added: 1 , Zero Std: 0 , Max Cor: 0.888
#>
43 <R=0.888,thr=0.800>, Top: 3< 1 >[Fa= 3923 ]( 3 , 3 , 3922 ),<|><>Tot Used: 6804 , Added: 3 , Zero Std: 0 , Max Cor: 0.800
#>
44 <R=0.800,thr=0.800>
#>
[ 44 ], 0.7999029 Decor Dimension: 6804 Nused: 6804 . Cor to Base: 2220 , ABase: 7748 , Outcome Base: 0
#>
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]
pander::pander(sum(apply(dataframe[,varlist],2,var)))63594442
pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))6628006
pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))3.08
pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))1.7
1.5.1 The decorrelation matrix
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
UPLTM <- attr(DEdataframe,"UPLTM")
gplots::heatmap.2(1.0*(abs(UPLTM)>0),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
}1.5.2 Formulas Network
Displaying the features associations
par(op)
if ((ncol(dataframe) < 1000) && (ncol(dataframe)>10))
{
DEdataframeB <- ILAA(dataframe,verbose=TRUE,thr=thro,bootstrap=30)
transform <- 1*(attr(DEdataframeB,"UPLTM") != 0)
print(ncol(transform))
thrcol <- 1 + 0.025*nrow(transform)
rsum <- apply(1*(transform !=0),1,sum) > 2
csum <- apply(1*(transform !=0),2,sum) > thrcol | rsum
transform <- transform[csum,csum]
csum <- (apply(1*(transform !=0),2,sum) > 1) & (apply(1*(transform !=0),1,sum) > 1)
transform <- transform[csum,csum]
print(ncol(transform))
if (ncol(transform)>100)
{
thrcol <- 1 + 0.10*nrow(transform)
rsum <- apply(1*(transform !=0),1,sum) > 4
csum <- apply(1*(transform !=0),2,sum) > thrcol | rsum
transform <- transform[csum,csum]
csum <- (apply(1*(transform !=0),2,sum) > 3) & (apply(1*(transform !=0),1,sum) > 3)
transform <- transform[csum,csum]
}
print(ncol(transform))
if (ncol(transform)>100)
{
thrcol <- 1 + 0.20*nrow(transform)
rsum <- apply(1*(transform !=0),1,sum) > 8
csum <- apply(1*(transform !=0),2,sum) > thrcol | rsum
transform <- transform[csum,csum]
csum <- (apply(1*(transform !=0),2,sum) > 7) & (apply(1*(transform !=0),1,sum) > 7)
transform <- transform[csum,csum]
}
print(ncol(transform))
if ((ncol(transform) > 10) && (ncol(transform) < 150))
{
gplots::heatmap.2(transform,
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Red Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
colnames(transform) <- str_remove_all(colnames(transform),"La_")
VertexSize <- apply(transform,2,mean)
VertexSize <- 5*VertexSize/max(VertexSize)
gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
gr$layout <- layout_with_fr
fc <- cluster_optimal(gr)
plot(fc, gr,
edge.width = 0.5*E(gr)$weight,
vertex.size=VertexSize,
edge.arrow.size=0.5,
edge.arrow.width=0.5,
vertex.label.cex=0.65,
vertex.label.dist=1,
main="Feature Association")
}
}
par(op)1.7 The correlation matrix after decorrelation
if (!largeSet)
{
cormat <- cor(DEdataframe[,varlistc],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Correlation after ILAA",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
par(op)
diag(cormat) <- 0
print(max(abs(cormat)))
}
1.8 U-MAP Visualization of features
1.8.1 The UMAP based on LASSO on Raw Data
if (nrow(dataframe) < 1000)
{
classes <- unique(dataframe[1:numsub,outcome])
raincolors <- rainbow(length(classes))
names(raincolors) <- classes
datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}
1.8.2 The decorralted UMAP
if (nrow(dataframe) < 1000)
{
datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}
1.9 Univariate Analysis
1.9.1 Univariate
univarRAW <- uniRankVar(varlist,
paste(outcome,"~1"),
outcome,
dataframe,
rankingTest="AUC")100 : V100 200 : V201 300 : V302 400 : V402 500 : V504
600 : V606 700 : V707 800 : V807 900 : V907 1000 : V1008
1100 : V1108 1200 : V1209 1300 : V1309 1400 : V1409 1500 : V1509
1600 : V1610 1700 : V1710 1800 : V1810 1900 : V1911 2000 : V2012
2100 : V2113 2200 : V2213 2300 : V2313 2400 : V2417 2500 : V2518
2600 : V2620 2700 : V2722 2800 : V2822 2900 : V2922 3000 : V3023
3100 : V3123 3200 : V3223 3300 : V3326 3400 : V3428 3500 : V3528
3600 : V3629 3700 : V3734 3800 : V3835 3900 : V3935 4000 : V4038
4100 : V4140 4200 : V4243 4300 : V4344 4400 : V4445 4500 : V4547
4600 : V4649 4700 : V4751 4800 : V4853 4900 : V4954 5000 : V5055
5100 : V5156 5200 : V5256 5300 : V5360 5400 : V5462 5500 : V5564
5600 : V5666 5700 : V5768 5800 : V5868 5900 : V5970 6000 : V6070
6100 : V6171 6200 : V6271 6300 : V6372 6400 : V6473 6500 : V6573
6600 : V6675 6700 : V6777 6800 : V6881 6900 : V6983 7000 : V7088
7100 : V7190 7200 : V7291 7300 : V7393 7400 : V7496 7500 : V7597
7600 : V7701 7700 : V7803 7800 : V7904 7900 : V8007 8000 : V8108
8100 : V8209 8200 : V8310 8300 : V8414 8400 : V8516 8500 : V8620
8600 : V8721 8700 : V8822 8800 : V8925 8900 : V9026 9000 : V9128
9100 : V9232 9200 : V9332 9300 : V9433 9400 : V9533 9500 : V9638
9600 : V9739 9700 : V9841 9800 : V9944
univarDe <- uniRankVar(varlistc,
paste(outcome,"~1"),
outcome,
DEdataframe,
rankingTest="AUC",
)100 : V100 200 : La_V201 300 : V302 400 : La_V402 500 : V504
600 : V606 700 : V707 800 : V807 900 : La_V907 1000 : La_V1008
1100 : La_V1108 1200 : V1209 1300 : La_V1309 1400 : La_V1409 1500 :
La_V1509
1600 : La_V1610 1700 : La_V1710 1800 : La_V1810 1900 : La_V1911 2000 :
La_V2012
2100 : La_V2113 2200 : La_V2213 2300 : V2313 2400 : La_V2417 2500 :
La_V2518
2600 : V2620 2700 : La_V2722 2800 : V2822 2900 : V2922 3000 :
La_V3023
3100 : La_V3123 3200 : La_V3223 3300 : V3326 3400 : V3428 3500 :
La_V3528
3600 : La_V3629 3700 : La_V3734 3800 : La_V3835 3900 : La_V3935 4000 :
La_V4038
4100 : La_V4140 4200 : La_V4243 4300 : V4344 4400 : V4445 4500 :
La_V4547
4600 : La_V4649 4700 : La_V4751 4800 : V4853 4900 : La_V4954 5000 :
La_V5055
5100 : V5156 5200 : La_V5256 5300 : V5360 5400 : La_V5462 5500 :
La_V5564
5600 : La_V5666 5700 : La_V5768 5800 : La_V5868 5900 : La_V5970 6000 :
La_V6070
6100 : La_V6171 6200 : La_V6271 6300 : La_V6372 6400 : La_V6473 6500 :
V6573
6600 : La_V6675 6700 : La_V6777 6800 : V6881 6900 : La_V6983 7000 :
La_V7088
7100 : La_V7190 7200 : V7291 7300 : La_V7393 7400 : La_V7496 7500 :
La_V7597
7600 : La_V7701 7700 : La_V7803 7800 : La_V7904 7900 : V8007 8000 :
La_V8108
8100 : La_V8209 8200 : La_V8310 8300 : La_V8414 8400 : La_V8516 8500 :
V8620
8600 : La_V8721 8700 : La_V8822 8800 : La_V8925 8900 : La_V9026 9000 :
V9128
9100 : La_V9232 9200 : La_V9332 9300 : La_V9433 9400 : V9533 9500 :
La_V9638
9600 : La_V9739 9700 : La_V9841 9800 : V9944
1.9.2 Final Table
univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")
##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| V5005 | 314.7 | 72.9 | 239 | 83.6 | 0.18466 | 0.772 |
| V4960 | 47.5 | 49.3 | 124 | 97.3 | 0.19534 | 0.751 |
| V2309 | 43.1 | 45.3 | 113 | 89.0 | 0.18665 | 0.751 |
| V8368 | 44.9 | 46.1 | 116 | 90.6 | 0.21091 | 0.751 |
| V312 | 47.2 | 48.0 | 122 | 94.7 | 0.21678 | 0.750 |
| V3365 | 46.3 | 46.9 | 119 | 92.5 | 0.22139 | 0.749 |
| V9617 | 40.9 | 44.7 | 109 | 87.5 | 0.15591 | 0.749 |
| V414 | 47.5 | 50.4 | 125 | 100.4 | 0.16265 | 0.749 |
| V9092 | 33.9 | 63.1 | 124 | 132.6 | 0.00199 | 0.748 |
| V1936 | 316.0 | 79.5 | 243 | 79.2 | 0.28495 | 0.748 |
topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]
pander::pander(finalTable)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| La_V2076 | -8.27 | 8.44 | 3.585 | 11.45 | 2.89e-09 | 0.794 |
| La_V2185 | 5.47 | 8.88 | -7.028 | 12.34 | 6.82e-04 | 0.785 |
| La_V3945 | 13.98 | 15.99 | -9.315 | 23.91 | 1.61e-05 | 0.780 |
| La_V3970 | -47.14 | 37.20 | -9.887 | 35.41 | 3.03e-01 | 0.775 |
| V5005 | 314.74 | 72.85 | 239.304 | 83.62 | 1.85e-01 | 0.772 |
| La_V7665 | 7.17 | 5.80 | 0.807 | 7.14 | 4.64e-01 | 0.771 |
| La_V8517 | 23.04 | 17.21 | 7.501 | 15.54 | 5.18e-03 | 0.766 |
| La_V1124 | -14.90 | 21.85 | 15.639 | 36.41 | 1.25e-06 | 0.760 |
| La_V3397 | -1.61 | 1.23 | -0.537 | 1.21 | 2.00e-01 | 0.757 |
| La_V3383 | 10.28 | 8.06 | 2.115 | 12.65 | 1.33e-02 | 0.753 |
dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")
pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))| mean | total | fraction |
|---|---|---|
| 3.22 | 6550 | 0.665 |
theCharformulas <- attr(dc,"LatentCharFormulas")
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])
orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")
finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])| DecorFormula | caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | RAWAUC | fscores | |
|---|---|---|---|---|---|---|---|---|---|
| La_V2076 | + V2076 - (0.907)V3417 | -8.27 | 8.44 | 3.585 | 11.45 | 2.89e-09 | 0.794 | 0.548 | 0 |
| La_V2185 | + (5.133)V1380 + V2185 - (3.675)V8390 - (2.486)V8743 | 5.47 | 8.88 | -7.028 | 12.34 | 6.82e-04 | 0.785 | 0.592 | -2 |
| La_V3945 | - (0.847)V1711 + V3945 | 13.98 | 15.99 | -9.315 | 23.91 | 1.61e-05 | 0.780 | 0.571 | 2 |
| La_V3970 | + V3970 - (1.111)V9179 | -47.14 | 37.20 | -9.887 | 35.41 | 3.03e-01 | 0.775 | 0.605 | -1 |
| V5005 | NA | 314.74 | 72.85 | 239.304 | 83.62 | 1.85e-01 | 0.772 | 0.772 | NA |
| V50051 | NA | 314.74 | 72.85 | 239.304 | 83.62 | 1.85e-01 | 0.772 | NA | NA |
| La_V7665 | - (0.147)V5844 + V7665 - (0.972)V9179 | 7.17 | 5.80 | 0.807 | 7.14 | 4.64e-01 | 0.771 | 0.514 | -2 |
| La_V8517 | - (0.947)V7611 + V8517 | 23.04 | 17.21 | 7.501 | 15.54 | 5.18e-03 | 0.766 | 0.615 | 3 |
| La_V1124 | + V1124 - (0.614)V7328 | -14.90 | 21.85 | 15.639 | 36.41 | 1.25e-06 | 0.760 | 0.505 | -1 |
| La_V3397 | + (0.489)V3001 + V3397 - (0.909)V7611 - (0.584)V8517 | -1.61 | 1.23 | -0.537 | 1.21 | 2.00e-01 | 0.757 | 0.604 | -2 |
| La_V3383 | + V3383 - (1.091)V3652 + (3.034)V4491 - (2.920)V6324 | 10.28 | 8.06 | 2.115 | 12.65 | 1.33e-02 | 0.753 | 0.507 | -1 |
| V4960 | NA | 47.51 | 49.25 | 123.696 | 97.33 | 1.95e-01 | 0.751 | 0.751 | NA |
| V2309 | NA | 43.06 | 45.32 | 112.616 | 89.00 | 1.87e-01 | 0.751 | 0.751 | NA |
| V8368 | NA | 44.89 | 46.06 | 116.036 | 90.62 | 2.11e-01 | 0.751 | 0.751 | NA |
| V312 | NA | 47.18 | 48.01 | 121.634 | 94.73 | 2.17e-01 | 0.750 | 0.750 | NA |
| V3365 | NA | 46.26 | 46.93 | 119.054 | 92.52 | 2.21e-01 | 0.749 | 0.749 | NA |
| V9617 | NA | 40.89 | 44.75 | 108.848 | 87.49 | 1.56e-01 | 0.749 | 0.749 | NA |
| V414 | NA | 47.47 | 50.45 | 125.348 | 100.36 | 1.63e-01 | 0.749 | 0.749 | NA |
| V9092 | NA | 33.89 | 63.11 | 123.607 | 132.62 | 1.99e-03 | 0.748 | 0.748 | NA |
| V1936 | NA | 315.95 | 79.48 | 243.062 | 79.21 | 2.85e-01 | 0.748 | 0.748 | NA |
1.10 Comparing ILAA vs PCA vs EFA
1.10.1 PCA
featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE) #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous])
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)
#pander::pander(pc$rotation)
PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])
gplots::heatmap.2(abs(PCACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "PCA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
1.10.2 EFA
EFAdataframe <- dataframeScaled
if (length(iscontinous) < 2000)
{
topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
if (topred < 2) topred <- 2
uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE) # EFA analysis
predEFA <- predict(uls,dataframeScaled[,iscontinous])
EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous])
EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
gplots::heatmap.2(abs(EFACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "EFA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
}1.11 Effect on CAR modeling
par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(rawmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
}
pander::pander(table(dataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 109 | 3 |
| 1 | 13 | 75 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.920 | 0.873 | 0.954 |
| 3 | se | 0.852 | 0.761 | 0.919 |
| 4 | sp | 0.973 | 0.924 | 0.994 |
| 6 | diag.or | 209.615 | 57.738 | 761.000 |
par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(IDeAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
}
pander::pander(table(DEdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 98 | 14 |
| 1 | 13 | 75 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.865 | 0.810 | 0.909 |
| 3 | se | 0.852 | 0.761 | 0.919 |
| 4 | sp | 0.875 | 0.799 | 0.930 |
| 6 | diag.or | 40.385 | 17.919 | 91.016 |
par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(PCAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}
pander::pander(table(PCAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 104 | 8 |
| 1 | 39 | 49 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.765 | 0.700 | 0.822 |
| 3 | se | 0.557 | 0.447 | 0.663 |
| 4 | sp | 0.929 | 0.864 | 0.969 |
| 6 | diag.or | 16.333 | 7.100 | 37.573 |
par(op)1.11.1 EFA
EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(EFAmodel,EFAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(EFAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
}
pander::pander(table(EFAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 109 | 3 |
| 1 | 13 | 75 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.920 | 0.873 | 0.954 |
| 3 | se | 0.852 | 0.761 | 0.919 |
| 4 | sp | 0.973 | 0.924 | 0.994 |
| 6 | diag.or | 209.615 | 57.738 | 761.000 |
par(op)